A hybrid stochastic method with adaptive time step control for reaction–diffusion systems

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)392-402
Journal / PublicationJournal of Computational Physics
Online published12 Dec 2018
Publication statusPublished - 15 Feb 2019


Randomness often plays an important role in the spatial and temporal dynamics of biological systems. General stochastic simulation methods may lead to excessive computational cost for a system in which a large number of molecules involved. Therefore, multi-scale hybrid simulation methods become important for stochastic simulations. Here we build a spatially hybrid method which couples two approaches: discrete stochastic simulation and continuous stochastic differential equations. In our method, the locations of the interfaces between the two approaches are changing according to the distribution of molecules in a one-dimensional domain. To balance the accuracy and efficiency, the time step of the numerical method for the continuous stochastic differential equations is adapted to the dynamics of the molecules near the adaptive interfaces. The simulation results for a linear system and two nonlinear biological systems in different one-dimensional domains demonstrate the effectiveness and advantage of our new hybrid method with the adaptive time step control.

Research Area(s)

  • Biological patterning, Hybrid method, Reaction–diffusion systems, Stochastic simulation